Search results for "Complex."
showing 10 items of 5824 documents
Transition Function Complexity of Finite Automata
2011
State complexity of finite automata in some cases gives the same complexity value for automata which intuitively seem to have completely different complexities. In this paper we consider a new measure of descriptional complexity of finite automata -- BC-complexity. Comparison of it with the state complexity is carried out here as well as some interesting minimization properties are discussed. It is shown that minimization of the number of states can lead to a superpolynomial increase of BC-complexity.
On t-covers in finite projective spaces
1979
A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.
On positive P
2002
Continuing a line of research opened up by Grigni and Sipser (1992) and further pursued by Stewart (1994), we show that a wide variety of equivalent characterizations of P still remain equivalent when restricted to be positive. All these restrictions thus define the same class posP, a proper subclass of monP, the class of monotone problems in P. We also exhibit complete problems for posP under very weak reductions.
Subvarieties of the Varieties Generated by the SuperalgebraM1, 1(E) orM2(𝒦)
2003
Abstract Let 𝒦 be a field of characteristic zero, and let us consider the matrix algebra M 2(𝒦) endowed with the ℤ2-grading (𝒦e 11 ⊕ 𝒦e 22) ⊕ (𝒦e 12 ⊕ 𝒦e 21). We define two superalgebras, ℛ p and 𝒮 q , where p and q are positive integers. We show that if 𝒰 is a proper subvariety of the variety generated by the superalgebra M 2(𝒦), then the even-proper part of the T 2-ideal of graded polynomial identities of 𝒰 asymptotically coincides with the even-proper part of the graded polynomial identities of the variety generated by the superalgebra ℛ p ⊕ 𝒮 q . This description also affords an even-asymptotic desc…
Codimension growth of two-dimensional non-associative algebras
2007
Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.
Incremental termination proofs and the length of derivations
1991
Incremental termination proofs, a concept similar to termination proofs by quasi-commuting orderings, are investigated. In particular, we show how an incremental termination proof for a term rewriting system T can be used to derive upper bounds on the length of derivations in T. A number of examples show that our results can be applied to yield (sharp) low-degree polynomial complexity bounds.
Lower space bounds for randomized computation
1994
It is a fundamental problem in the randomized computation how to separate different randomized time or randomized space classes (c.f., e.g., [KV87, KV88]). We have separated randomized space classes below log n in [FK94]. Now we have succeeded to separate small randomized time classes for multi-tape 2-way Turing machines. Surprisingly, these “small” bounds are of type n+f(n) with f(n) not exceeding linear functions. This new approach to “sublinear” time complexity is a natural counterpart to sublinear space complexity. The latter was introduced by considering the input tape and the work tape as separate devices and distinguishing between the space used for processing information and the spa…
Padding and the expressive power of existential second-order logics
1998
Padding techniques are well-known from Computational Complexity Theory. Here, an analogous concept is considered in the context of existential second-order logics. Informally, a graph H is a padded version of a graph G, if H consists of an isomorphic copy of G and some isolated vertices. A set A of graphs is called weakly expressible by a formula ϕ in the presence of padding, if ϕ is able to distinguish between (sufficiently) padded versions of graphs from A and padded versions of graphs that are not in A.
Reordering Method and Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams
2017
We consider Quantum OBDD model. It is restricted version of read-once Quantum Branching Programs, with respect to “width” complexity. It is known that maximal complexity gap between deterministic and quantum model is exponential. But there are few examples of such functions. We present method (called “reordering”), which allows to build Boolean function g from Boolean Function f, such that if for f we have gap between quantum and deterministic OBDD complexity for natural order of variables, then we have almost the same gap for function g, but for any order. Using it we construct the total function REQ which deterministic OBDD complexity is \(2^{\varOmega (n/log n)}\) and present quantum OBD…
If P ≠ NP then Some Strongly Noninvertible Functions Are Invertible
2001
Rabi, Rivest, and Sherman alter the standard notion of noninvertibility to a new notion they call strong noninvertibility, and show--via explicit cryptographic protocols for secret-key agreement ([RS93, RS97] attribute this to Rivest and Sherman) and digital signatures [RS93, RS97]--that strongly noninvertible functions would be very useful components in protocol design. Their definition of strong noninvertibility has a small twist ("respecting the argument given") that is needed to ensure cryptographic usefulness. In this paper, we show that this small twist has a large, unexpected consequence: Unless P = NP, some strongly noninvertible functions are invertible.